Identifier
Mp00058:
Perfect matchings
—to permutation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00069: Permutations —complement⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0012;cc-rep-0
[(1,2)]=>[2,1]=>[1,2]=>[2]
[(1,2),(3,4)]=>[2,1,4,3]=>[3,4,1,2]=>[2,2]
[(1,3),(2,4)]=>[3,4,1,2]=>[2,1,4,3]=>[1,2,1]
[(1,4),(2,3)]=>[4,3,2,1]=>[1,2,3,4]=>[4]
[(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[2,2,2]
[(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[1,2,1,2]
[(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>[4,2]
[(1,5),(2,3),(4,6)]=>[5,3,2,6,1,4]=>[2,4,5,1,6,3]=>[3,2,1]
[(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>[3,3]
[(1,6),(2,4),(3,5)]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[2,2,2]
[(1,5),(2,4),(3,6)]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>[2,3,1]
[(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[1,1,2,1,1]
[(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>[1,2,2,1]
[(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[2,1,2,1]
[(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>[2,4]
[(1,3),(2,6),(4,5)]=>[3,6,1,5,4,2]=>[4,1,6,2,3,5]=>[1,2,3]
[(1,4),(2,6),(3,5)]=>[4,6,5,1,3,2]=>[3,1,2,6,4,5]=>[1,3,2]
[(1,5),(2,6),(3,4)]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[1,4,1]
[(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6]
[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]
[(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[6,5,8,7,3,4,1,2]=>[1,2,1,2,2]
[(1,4),(2,3),(5,6),(7,8)]=>[4,3,2,1,6,5,8,7]=>[5,6,7,8,3,4,1,2]=>[4,2,2]
[(1,5),(2,3),(4,6),(7,8)]=>[5,3,2,6,1,4,8,7]=>[4,6,7,3,8,5,1,2]=>[3,2,1,2]
[(1,6),(2,3),(4,5),(7,8)]=>[6,3,2,5,4,1,8,7]=>[3,6,7,4,5,8,1,2]=>[3,3,2]
[(1,7),(2,3),(4,5),(6,8)]=>[7,3,2,5,4,8,1,6]=>[2,6,7,4,5,1,8,3]=>[3,2,2,1]
[(1,8),(2,3),(4,5),(6,7)]=>[8,3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3,8]=>[3,2,3]
[(1,8),(2,4),(3,5),(6,7)]=>[8,4,5,2,3,7,6,1]=>[1,5,4,7,6,2,3,8]=>[2,2,1,3]
[(1,7),(2,4),(3,5),(6,8)]=>[7,4,5,2,3,8,1,6]=>[2,5,4,7,6,1,8,3]=>[2,2,1,2,1]
[(1,6),(2,4),(3,5),(7,8)]=>[6,4,5,2,3,1,8,7]=>[3,5,4,7,6,8,1,2]=>[2,2,2,2]
[(1,5),(2,4),(3,6),(7,8)]=>[5,4,6,2,1,3,8,7]=>[4,5,3,7,8,6,1,2]=>[2,3,1,2]
[(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[5,4,3,8,7,6,1,2]=>[1,1,2,1,1,2]
[(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[6,4,8,3,7,5,1,2]=>[1,2,2,1,2]
[(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[7,8,4,3,6,5,1,2]=>[2,1,2,1,2]
[(1,2),(3,6),(4,5),(7,8)]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[2,4,2]
[(1,3),(2,6),(4,5),(7,8)]=>[3,6,1,5,4,2,8,7]=>[6,3,8,4,5,7,1,2]=>[1,2,3,2]
[(1,4),(2,6),(3,5),(7,8)]=>[4,6,5,1,3,2,8,7]=>[5,3,4,8,6,7,1,2]=>[1,3,2,2]
[(1,5),(2,6),(3,4),(7,8)]=>[5,6,4,3,1,2,8,7]=>[4,3,5,6,8,7,1,2]=>[1,4,1,2]
[(1,6),(2,5),(3,4),(7,8)]=>[6,5,4,3,2,1,8,7]=>[3,4,5,6,7,8,1,2]=>[6,2]
[(1,7),(2,5),(3,4),(6,8)]=>[7,5,4,3,2,8,1,6]=>[2,4,5,6,7,1,8,3]=>[5,2,1]
[(1,8),(2,5),(3,4),(6,7)]=>[8,5,4,3,2,7,6,1]=>[1,4,5,6,7,2,3,8]=>[5,3]
[(1,8),(2,6),(3,4),(5,7)]=>[8,6,4,3,7,2,5,1]=>[1,3,5,6,2,7,4,8]=>[4,2,2]
[(1,7),(2,6),(3,4),(5,8)]=>[7,6,4,3,8,2,1,5]=>[2,3,5,6,1,7,8,4]=>[4,3,1]
[(1,6),(2,7),(3,4),(5,8)]=>[6,7,4,3,8,1,2,5]=>[3,2,5,6,1,8,7,4]=>[1,3,2,1,1]
[(1,5),(2,7),(3,4),(6,8)]=>[5,7,4,3,1,8,2,6]=>[4,2,5,6,8,1,7,3]=>[1,4,2,1]
[(1,4),(2,7),(3,5),(6,8)]=>[4,7,5,1,3,8,2,6]=>[5,2,4,8,6,1,7,3]=>[1,3,1,2,1]
[(1,3),(2,7),(4,5),(6,8)]=>[3,7,1,5,4,8,2,6]=>[6,2,8,4,5,1,7,3]=>[1,2,2,2,1]
[(1,2),(3,7),(4,5),(6,8)]=>[2,1,7,5,4,8,3,6]=>[7,8,2,4,5,1,6,3]=>[2,3,2,1]
[(1,2),(3,8),(4,5),(6,7)]=>[2,1,8,5,4,7,6,3]=>[7,8,1,4,5,2,3,6]=>[2,3,3]
[(1,3),(2,8),(4,5),(6,7)]=>[3,8,1,5,4,7,6,2]=>[6,1,8,4,5,2,3,7]=>[1,2,2,3]
[(1,4),(2,8),(3,5),(6,7)]=>[4,8,5,1,3,7,6,2]=>[5,1,4,8,6,2,3,7]=>[1,3,1,3]
[(1,5),(2,8),(3,4),(6,7)]=>[5,8,4,3,1,7,6,2]=>[4,1,5,6,8,2,3,7]=>[1,4,3]
[(1,6),(2,8),(3,4),(5,7)]=>[6,8,4,3,7,1,5,2]=>[3,1,5,6,2,8,4,7]=>[1,3,2,2]
[(1,7),(2,8),(3,4),(5,6)]=>[7,8,4,3,6,5,1,2]=>[2,1,5,6,3,4,8,7]=>[1,3,3,1]
[(1,8),(2,7),(3,4),(5,6)]=>[8,7,4,3,6,5,2,1]=>[1,2,5,6,3,4,7,8]=>[4,4]
[(1,8),(2,7),(3,5),(4,6)]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>[3,2,3]
[(1,7),(2,8),(3,5),(4,6)]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[1,2,2,2,1]
[(1,6),(2,8),(3,5),(4,7)]=>[6,8,5,7,3,1,4,2]=>[3,1,4,2,6,8,5,7]=>[1,2,3,2]
[(1,5),(2,8),(3,6),(4,7)]=>[5,8,6,7,1,3,4,2]=>[4,1,3,2,8,6,5,7]=>[1,2,2,1,2]
[(1,4),(2,8),(3,6),(5,7)]=>[4,8,6,1,7,3,5,2]=>[5,1,3,8,2,6,4,7]=>[1,3,2,2]
[(1,3),(2,8),(4,6),(5,7)]=>[3,8,1,6,7,4,5,2]=>[6,1,8,3,2,5,4,7]=>[1,2,1,2,2]
[(1,2),(3,8),(4,6),(5,7)]=>[2,1,8,6,7,4,5,3]=>[7,8,1,3,2,5,4,6]=>[2,2,2,2]
[(1,2),(3,7),(4,6),(5,8)]=>[2,1,7,6,8,4,3,5]=>[7,8,2,3,1,5,6,4]=>[2,2,3,1]
[(1,3),(2,7),(4,6),(5,8)]=>[3,7,1,6,8,4,2,5]=>[6,2,8,3,1,5,7,4]=>[1,2,1,3,1]
[(1,4),(2,7),(3,6),(5,8)]=>[4,7,6,1,8,3,2,5]=>[5,2,3,8,1,6,7,4]=>[1,3,3,1]
[(1,5),(2,7),(3,6),(4,8)]=>[5,7,6,8,1,3,2,4]=>[4,2,3,1,8,6,7,5]=>[1,2,2,2,1]
[(1,6),(2,7),(3,5),(4,8)]=>[6,7,5,8,3,1,2,4]=>[3,2,4,1,6,8,7,5]=>[1,2,3,1,1]
[(1,7),(2,6),(3,5),(4,8)]=>[7,6,5,8,3,2,1,4]=>[2,3,4,1,6,7,8,5]=>[3,4,1]
[(1,8),(2,6),(3,5),(4,7)]=>[8,6,5,7,3,2,4,1]=>[1,3,4,2,6,7,5,8]=>[3,3,2]
[(1,8),(2,5),(3,6),(4,7)]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[2,1,2,1,2]
[(1,7),(2,5),(3,6),(4,8)]=>[7,5,6,8,2,3,1,4]=>[2,4,3,1,7,6,8,5]=>[2,1,2,2,1]
[(1,6),(2,5),(3,7),(4,8)]=>[6,5,7,8,2,1,3,4]=>[3,4,2,1,7,8,6,5]=>[2,1,3,1,1]
[(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1]
[(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[5,3,2,8,1,7,6,4]=>[1,1,2,2,1,1]
[(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[6,3,8,2,1,7,5,4]=>[1,2,1,2,1,1]
[(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[7,8,3,2,1,6,5,4]=>[2,1,1,2,1,1]
[(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[7,8,4,2,6,1,5,3]=>[2,1,2,2,1]
[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[6,4,8,2,7,1,5,3]=>[1,2,2,2,1]
[(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[5,4,2,8,7,1,6,3]=>[1,1,2,1,2,1]
[(1,5),(2,4),(3,7),(6,8)]=>[5,4,7,2,1,8,3,6]=>[4,5,2,7,8,1,6,3]=>[2,3,2,1]
[(1,6),(2,4),(3,7),(5,8)]=>[6,4,7,2,8,1,3,5]=>[3,5,2,7,1,8,6,4]=>[2,2,2,1,1]
[(1,7),(2,4),(3,6),(5,8)]=>[7,4,6,2,8,3,1,5]=>[2,5,3,7,1,6,8,4]=>[2,2,3,1]
[(1,8),(2,4),(3,6),(5,7)]=>[8,4,6,2,7,3,5,1]=>[1,5,3,7,2,6,4,8]=>[2,2,2,2]
[(1,8),(2,3),(4,6),(5,7)]=>[8,3,2,6,7,4,5,1]=>[1,6,7,3,2,5,4,8]=>[3,1,2,2]
[(1,7),(2,3),(4,6),(5,8)]=>[7,3,2,6,8,4,1,5]=>[2,6,7,3,1,5,8,4]=>[3,1,3,1]
[(1,6),(2,3),(4,7),(5,8)]=>[6,3,2,7,8,1,4,5]=>[3,6,7,2,1,8,5,4]=>[3,1,2,1,1]
[(1,5),(2,3),(4,7),(6,8)]=>[5,3,2,7,1,8,4,6]=>[4,6,7,2,8,1,5,3]=>[3,2,2,1]
[(1,4),(2,3),(5,7),(6,8)]=>[4,3,2,1,7,8,5,6]=>[5,6,7,8,2,1,4,3]=>[4,1,2,1]
[(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[6,5,8,7,2,1,4,3]=>[1,2,1,1,2,1]
[(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[7,8,5,6,2,1,4,3]=>[2,2,1,2,1]
[(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,8,7,6,5]=>[7,8,5,6,1,2,3,4]=>[2,2,4]
[(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,8,7,6,5]=>[6,5,8,7,1,2,3,4]=>[1,2,1,4]
[(1,4),(2,3),(5,8),(6,7)]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[4,4]
[(1,5),(2,3),(4,8),(6,7)]=>[5,3,2,8,1,7,6,4]=>[4,6,7,1,8,2,3,5]=>[3,2,3]
[(1,6),(2,3),(4,8),(5,7)]=>[6,3,2,8,7,1,5,4]=>[3,6,7,1,2,8,4,5]=>[3,3,2]
[(1,7),(2,3),(4,8),(5,6)]=>[7,3,2,8,6,5,1,4]=>[2,6,7,1,3,4,8,5]=>[3,4,1]
[(1,8),(2,3),(4,7),(5,6)]=>[8,3,2,7,6,5,4,1]=>[1,6,7,2,3,4,5,8]=>[3,5]
[(1,8),(2,4),(3,7),(5,6)]=>[8,4,7,2,6,5,3,1]=>[1,5,2,7,3,4,6,8]=>[2,2,4]
[(1,7),(2,4),(3,8),(5,6)]=>[7,4,8,2,6,5,1,3]=>[2,5,1,7,3,4,8,6]=>[2,2,3,1]
[(1,6),(2,4),(3,8),(5,7)]=>[6,4,8,2,7,1,5,3]=>[3,5,1,7,2,8,4,6]=>[2,2,2,2]
[(1,5),(2,4),(3,8),(6,7)]=>[5,4,8,2,1,7,6,3]=>[4,5,1,7,8,2,3,6]=>[2,3,3]
[(1,4),(2,5),(3,8),(6,7)]=>[4,5,8,1,2,7,6,3]=>[5,4,1,8,7,2,3,6]=>[1,1,2,1,3]
[(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,8,2,7,6,4]=>[6,4,8,1,7,2,3,5]=>[1,2,2,3]
[(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,8,3,7,6,4]=>[7,8,4,1,6,2,3,5]=>[2,1,2,3]
[(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,8,7,3,5,4]=>[7,8,3,1,2,6,4,5]=>[2,1,3,2]
[(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,8,7,2,5,4]=>[6,3,8,1,2,7,4,5]=>[1,2,3,2]
[(1,4),(2,6),(3,8),(5,7)]=>[4,6,8,1,7,2,5,3]=>[5,3,1,8,2,7,4,6]=>[1,1,2,2,2]
[(1,5),(2,6),(3,8),(4,7)]=>[5,6,8,7,1,2,4,3]=>[4,3,1,2,8,7,5,6]=>[1,1,3,1,2]
[(1,6),(2,5),(3,8),(4,7)]=>[6,5,8,7,2,1,4,3]=>[3,4,1,2,7,8,5,6]=>[2,4,2]
[(1,7),(2,5),(3,8),(4,6)]=>[7,5,8,6,2,4,1,3]=>[2,4,1,3,7,5,8,6]=>[2,3,2,1]
[(1,8),(2,5),(3,7),(4,6)]=>[8,5,7,6,2,4,3,1]=>[1,4,2,3,7,5,6,8]=>[2,3,3]
[(1,8),(2,6),(3,7),(4,5)]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>[2,4,2]
[(1,7),(2,6),(3,8),(4,5)]=>[7,6,8,5,4,2,1,3]=>[2,3,1,4,5,7,8,6]=>[2,5,1]
[(1,6),(2,7),(3,8),(4,5)]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[1,1,4,1,1]
[(1,5),(2,7),(3,8),(4,6)]=>[5,7,8,6,1,4,2,3]=>[4,2,1,3,8,5,7,6]=>[1,1,3,2,1]
[(1,4),(2,7),(3,8),(5,6)]=>[4,7,8,1,6,5,2,3]=>[5,2,1,8,3,4,7,6]=>[1,1,2,3,1]
[(1,3),(2,7),(4,8),(5,6)]=>[3,7,1,8,6,5,2,4]=>[6,2,8,1,3,4,7,5]=>[1,2,4,1]
[(1,2),(3,7),(4,8),(5,6)]=>[2,1,7,8,6,5,3,4]=>[7,8,2,1,3,4,6,5]=>[2,1,4,1]
[(1,2),(3,8),(4,7),(5,6)]=>[2,1,8,7,6,5,4,3]=>[7,8,1,2,3,4,5,6]=>[2,6]
[(1,3),(2,8),(4,7),(5,6)]=>[3,8,1,7,6,5,4,2]=>[6,1,8,2,3,4,5,7]=>[1,2,5]
[(1,4),(2,8),(3,7),(5,6)]=>[4,8,7,1,6,5,3,2]=>[5,1,2,8,3,4,6,7]=>[1,3,4]
[(1,5),(2,8),(3,7),(4,6)]=>[5,8,7,6,1,4,3,2]=>[4,1,2,3,8,5,6,7]=>[1,4,3]
[(1,6),(2,8),(3,7),(4,5)]=>[6,8,7,5,4,1,3,2]=>[3,1,2,4,5,8,6,7]=>[1,5,2]
[(1,7),(2,8),(3,6),(4,5)]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>[1,6,1]
[(1,8),(2,7),(3,6),(4,5)]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8]
[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2]
[(1,8),(2,7),(3,6),(4,5),(9,10)]=>[8,7,6,5,4,3,2,1,10,9]=>[3,4,5,6,7,8,9,10,1,2]=>[8,2]
[(1,10),(2,9),(3,8),(4,6),(5,7)]=>[10,9,8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8,9,10]=>[4,2,4]
[(1,10),(2,8),(3,9),(4,6),(5,7)]=>[10,8,9,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,9,8,10]=>[2,2,2,2,2]
[(1,4),(2,3),(5,10),(6,9),(7,8)]=>[4,3,2,1,10,9,8,7,6,5]=>[7,8,9,10,1,2,3,4,5,6]=>[4,6]
[(1,10),(2,8),(3,9),(4,7),(5,6)]=>[10,8,9,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,9,8,10]=>[2,6,2]
[(1,2),(3,10),(4,9),(5,8),(6,7)]=>[2,1,10,9,8,7,6,5,4,3]=>[9,10,1,2,3,4,5,6,7,8]=>[2,8]
[(1,10),(2,9),(3,8),(4,7),(5,6)]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[10]
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2,2]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[1,1,1,1,1,2,1,1,1,1,1]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
searching the database
Sorry, this map was not found in the database.